lobatto_polynomial, a FORTRAN77 code which evaluates the completed Lobatto polynomial and associated functions.
The completed Lobatto polynomial Lo(n,x) can be defined by:
Lo(n,x) = n * ( P(n-1,x) - x * P(n,x) )
where n is a positive integer called the order, x is a real value
between -1 and +1, and P(n,x) is the Legendre polynomial.
The completed Lobatto polynomial Lo(n,x) has degree n+1, and is zero at x = -1 and x = +1.
gnuplot() is used to create images of some of the functions.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
lobatto_polynomial is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
bernstein_polynomial, a FORTRAN77 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
chebyshev_polynomial, a FORTRAN77 library which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.
GNUPLOT, FORTRAN77 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.
HERMITE_POLYNOMIAL, a FORTRAN77 library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
JACOBI_POLYNOMIAL, a FORTRAN77 library which evaluates the Jacobi polynomial and associated functions.
LAGUERRE_POLYNOMIAL, a FORTRAN77 library which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.
LEGENDRE_POLYNOMIAL, a FORTRAN77 library which evaluates the Legendre polynomial and associated functions.
POLPAK, a FORTRAN77 library which evaluates a variety of mathematical functions.
TEST_VALUES, a FORTRAN77 library which supplies test values of various mathematical functions.